You are speaking about dye sublimation printers, in all probability.
Like inkjet, the answer is it depends, in terms of how fade resistant
they are.
Earlier models were terrible, in fact, they were originally used in
the industry principally for proofing with warning not to leave them
exposed to light if you wanted to use them for any color matching. The way
they work is there is a continuous roll of film, slightly
larger in width than the print width they can produce. This roll
contains panels of dye in sequences of CMY and sometimes K, and
sometimes a clear topcoat.
The process they uses is each panel is set into place above a
specialty transfer paper which has a surface designed to accept
sublimated dye. Sublimation is the process of a material going
directly from a solid to gaseous state without passing through a
liquid phase. Using a special head with heating elements, similar in
some ways to a thermal fax machine head, but with usually 64/128 or
256 heat levels, the head translates the image line by line into heat
ranges which heats the dye which is held very close to the transfer
paper. The dye then is deposed onto the receptive surface of the
paper in differing densities.
This process is repeated with each dye panel, moving the paper into
the print path 3, 5 or 5 times depending upon how many panels are
involved, building up the colors, and coating.
The results, being continuos tone, are usually very smooth looking,
and the surface of the paper is usually photo-glossy.
Although costs have dropped on the consumables, it is still an
expensive printing technique. The panel set can only be used once
per print, and if you are printing one tiny dot of color in the
middle of the print and nothing more, you still use up a full panel
set of dye inks or that one print. Paper choice is usually limited
to one or possibly two surfaces.
To improve permanence, many use a UV clear coat layer as the last
panel to coat the print. You see, the problem is, the very nature of
dye sublimation is the dyes are designed to with heat dissipate into a
gaseous state.
However, dye sublimation dyes have become better, and, although I
would be surprised they meet the permanence of most pigment ink sets,
some newer ones are probably good for dozens of years in dark keeping.
I think the Kodak "instant" prints they offer in those kiosks in
department stores are dye sub and they do claim fairly lengthy
permanence now. Older versions of dye sub printers, even those by
Kodak were fugitive, however.
Art